{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "Until now, you've always used Gradient Descent to update the parameters and minimize the cost. In this notebook, you will learn more advanced optimization methods that can speed up learning and perhaps even get you to a better final value for the cost function. Having a good optimization algorithm can be the difference between waiting days vs. just a few hours to get a good result. \n",
    "\n",
    "Gradient descent goes \"downhill\" on a cost function $J$. Think of it as trying to do this: \n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Minimizing the cost is like finding the lowest point in a hilly landscape**<br> At each step of the training, you update your parameters following a certain direction to try to get to the lowest possible point. </center></caption>\n",
    "\n",
    "**Notations**: As usual, $\\frac{\\partial J}{\\partial a } = $ `da` for any variable `a`.\n",
    "\n",
    "To get started, run the following code to import the libraries you will need."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "Until now, you've always used Gradient Descent to update the parameters and minimize the cost. In this notebook, you will learn more advanced optimization methods that can speed up learning and perhaps even get you to a better final value for the cost function. Having a good optimization algorithm can be the difference between waiting days vs. just a few hours to get a good result. \n",
    "\n",
    "Gradient descent goes \"downhill\" on a cost function $J$. Think of it as trying to do this: \n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Minimizing the cost is like finding the lowest point in a hilly landscape**<br> At each step of the training, you update your parameters following a certain direction to try to get to the lowest possible point. </center></caption>\n",
    "\n",
    "**Notations**: As usual, $\\frac{\\partial J}{\\partial a } = $ `da` for any variable `a`.\n",
    "\n",
    "To get started, run the following code to import the libraries you will need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\program_files\\anaconda\\lib\\site-packages\\h5py\\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "import math\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "\n",
    "from opt_utils import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils import compute_cost, predict, predict_dec, plot_decision_boundary, load_dataset\n",
    "from testCases import *\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Gradient Descent\n",
    "\n",
    "A simple optimization method in machine learning is gradient descent (GD). When you take gradient steps with respect to all $m$ examples on each step, it is also called Batch Gradient Descent. \n",
    "\n",
    "**Warm-up exercise**: Implement the gradient descent update rule. The  gradient descent rule is, for $l = 1, ..., L$: \n",
    "$$ W^{[l]} = W^{[l]} - \\alpha \\text{ } dW^{[l]} \\tag{1}$$\n",
    "$$ b^{[l]} = b^{[l]} - \\alpha \\text{ } db^{[l]} \\tag{2}$$\n",
    "\n",
    "where L is the number of layers and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary. Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_gd\n",
    "\n",
    "def update_parameters_with_gd(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using one step of gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters to be updated:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients to update each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "\n",
    "    # Update rule for each parameter\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] -=  learning_rate * grads['dW'+str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] -= learning_rate *grads['db'+str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 = [[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 = [[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 = [[-0.88020257]\n",
      " [ 0.02561572]\n",
      " [ 0.57539477]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, learning_rate = update_parameters_with_gd_test_case()\n",
    "\n",
    "parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74604067]\n",
    " [-0.75184921]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variant of this is Stochastic Gradient Descent (SGD), which is equivalent to mini-batch gradient descent where each mini-batch has just 1 example. The update rule that you have just implemented does not change. What changes is that you would be computing gradients on just one training example at a time, rather than on the whole training set. The code examples below illustrate the difference between stochastic gradient descent and (batch) gradient descent. \n",
    "\n",
    "- **(Batch) Gradient Descent**:\n",
    "\n",
    "``` python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    # Forward propagation\n",
    "    a, caches = forward_propagation(X, parameters)\n",
    "    # Compute cost.\n",
    "    cost = compute_cost(a, Y)\n",
    "    # Backward propagation.\n",
    "    grads = backward_propagation(a, caches, parameters)\n",
    "    # Update parameters.\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "```\n",
    "\n",
    "- **Stochastic Gradient Descent**:\n",
    "\n",
    "```python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    for j in range(0, m):\n",
    "        # Forward propagation\n",
    "        a, caches = forward_propagation(X[:,j], parameters)\n",
    "        # Compute cost\n",
    "        cost = compute_cost(a, Y[:,j])\n",
    "        # Backward propagation\n",
    "        grads = backward_propagation(a, caches, parameters)\n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Stochastic Gradient Descent, you use only 1 training example before updating the gradients. When the training set is large, SGD can be faster. But the parameters will \"oscillate\" toward the minimum rather than converge smoothly. Here is an illustration of this: \n",
    "\n",
    "<img src=\"images/kiank_sgd.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 1** </u><font color='purple'>  : **SGD vs GD**<br> \"+\" denotes a minimum of the cost. SGD leads to many oscillations to reach convergence. But each step is a lot faster to compute for SGD than for GD, as it uses only one training example (vs. the whole batch for GD). </center></caption>\n",
    "\n",
    "**Note** also that implementing SGD requires 3 for-loops in total:\n",
    "1. Over the number of iterations\n",
    "2. Over the $m$ training examples\n",
    "3. Over the layers (to update all parameters, from $(W^{[1]},b^{[1]})$ to $(W^{[L]},b^{[L]})$)\n",
    "\n",
    "In practice, you'll often get faster results if you do not use neither the whole training set, nor only one training example, to perform each update. Mini-batch gradient descent uses an intermediate number of examples for each step. With mini-batch gradient descent, you loop over the mini-batches instead of looping over individual training examples.\n",
    "\n",
    "<img src=\"images/kiank_minibatch.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 2** </u>: <font color='purple'>  **SGD vs Mini-Batch GD**<br> \"+\" denotes a minimum of the cost. Using mini-batches in your optimization algorithm often leads to faster optimization. </center></caption>\n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- The difference between gradient descent, mini-batch gradient descent and stochastic gradient descent is the number of examples you use to perform one update step.\n",
    "- You have to tune a learning rate hyperparameter $\\alpha$.\n",
    "- With a well-turned mini-batch size, usually it outperforms either gradient descent or stochastic gradient descent (particularly when the training set is large)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Mini-Batch Gradient descent\n",
    "\n",
    "Let's learn how to build mini-batches from the training set (X, Y).\n",
    "\n",
    "There are two steps:\n",
    "- **Shuffle**: Create a shuffled version of the training set (X, Y) as shown below. Each column of X and Y represents a training example. Note that the random shuffling is done synchronously between X and Y. Such that after the shuffling the $i^{th}$ column of X is the example corresponding to the $i^{th}$ label in Y. The shuffling step ensures that examples will be split randomly into different mini-batches. \n",
    "\n",
    "<img src=\"images/kiank_shuffle.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "- **Partition**: Partition the shuffled (X, Y) into mini-batches of size `mini_batch_size` (here 64). Note that the number of training examples is not always divisible by `mini_batch_size`. The last mini batch might be smaller, but you don't need to worry about this. When the final mini-batch is smaller than the full `mini_batch_size`, it will look like this: \n",
    "\n",
    "<img src=\"images/kiank_partition.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "**Exercise**: Implement `random_mini_batches`. We coded the shuffling part for you. To help you with the partitioning step, we give you the following code that selects the indexes for the $1^{st}$ and $2^{nd}$ mini-batches:\n",
    "```python\n",
    "first_mini_batch_X = shuffled_X[:, 0 : mini_batch_size]\n",
    "second_mini_batch_X = shuffled_X[:, mini_batch_size : 2 * mini_batch_size]\n",
    "...\n",
    "```\n",
    "\n",
    "Note that the last mini-batch might end up smaller than `mini_batch_size=64`. Let $\\lfloor s \\rfloor$ represents $s$ rounded down to the nearest integer (this is `math.floor(s)` in Python). If the total number of examples is not a multiple of `mini_batch_size=64` then there will be $\\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$ mini-batches with a full 64 examples, and the number of examples in the final mini-batch will be ($m-mini_\\_batch_\\_size \\times \\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: random_mini_batches\n",
    "\n",
    "def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m))\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation].reshape((1,m))\n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, k*mini_batch_size:(k+1)*mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:, k*mini_batch_size:(k+1)*mini_batch_size]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, mini_batch_size*num_complete_minibatches:m]\n",
    "        mini_batch_Y = shuffled_Y[:, mini_batch_size*num_complete_minibatches:m]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of the 1st mini_batch_X: (12288, 64)\n",
      "shape of the 2nd mini_batch_X: (12288, 64)\n",
      "shape of the 3rd mini_batch_X: (12288, 20)\n",
      "shape of the 1st mini_batch_Y: (1, 64)\n",
      "shape of the 2nd mini_batch_Y: (1, 64)\n",
      "shape of the 3rd mini_batch_Y: (1, 20)\n",
      "mini batch sanity check: [ 0.90085595 -0.7612069   0.2344157 ]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()\n",
    "mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)\n",
    "\n",
    "print (\"shape of the 1st mini_batch_X: \" + str(mini_batches[0][0].shape))\n",
    "print (\"shape of the 2nd mini_batch_X: \" + str(mini_batches[1][0].shape))\n",
    "print (\"shape of the 3rd mini_batch_X: \" + str(mini_batches[2][0].shape))\n",
    "print (\"shape of the 1st mini_batch_Y: \" + str(mini_batches[0][1].shape))\n",
    "print (\"shape of the 2nd mini_batch_Y: \" + str(mini_batches[1][1].shape)) \n",
    "print (\"shape of the 3rd mini_batch_Y: \" + str(mini_batches[2][1].shape))\n",
    "print (\"mini batch sanity check: \" + str(mini_batches[0][0][0][0:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\"> \n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_X** </td> \n",
    "           <td > (12288, 20) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_Y** </td> \n",
    "           <td > (1, 20) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **mini batch sanity check** </td> \n",
    "           <td > [ 0.90085595 -0.7612069   0.2344157 ] </td> \n",
    "    </tr>\n",
    "    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Shuffling and Partitioning are the two steps required to build mini-batches\n",
    "- Powers of two are often chosen to be the mini-batch size, e.g., 16, 32, 64, 128."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Momentum\n",
    "\n",
    "Because mini-batch gradient descent makes a parameter update after seeing just a subset of examples, the direction of the update has some variance, and so the path taken by mini-batch gradient descent will \"oscillate\" toward convergence. Using momentum can reduce these oscillations. \n",
    "\n",
    "Momentum takes into account the past gradients to smooth out the update. We will store the 'direction' of the previous gradients in the variable $v$. Formally, this will be the exponentially weighted average of the gradient on previous steps. You can also think of $v$ as the \"velocity\" of a ball rolling downhill, building up speed (and momentum) according to the direction of the gradient/slope of the hill. \n",
    "\n",
    "<img src=\"images/opt_momentum.png\" style=\"width:400px;height:250px;\">\n",
    "<caption><center> <u><font color='purple'>**Figure 3**</u><font color='purple'>: The red arrows shows the direction taken by one step of mini-batch gradient descent with momentum. The blue points show the direction of the gradient (with respect to the current mini-batch) on each step. Rather than just following the gradient, we let the gradient influence $v$ and then take a step in the direction of $v$.<br> <font color='black'> </center>\n",
    "\n",
    "\n",
    "**Exercise**: Initialize the velocity. The velocity, $v$, is a python dictionary that needs to be initialized with arrays of zeros. Its keys are the same as those in the `grads` dictionary, that is:\n",
    "for $l =1,...,L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "```\n",
    "**Note** that the iterator l starts at 0 in the for loop while the first parameters are v[\"dW1\"] and v[\"db1\"] (that's a \"one\" on the superscript). This is why we are shifting l to l+1 in the `for` loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_velocity\n",
    "\n",
    "def initialize_velocity(parameters):\n",
    "    \"\"\"\n",
    "    Initializes the velocity as a python dictionary with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    \n",
    "    Returns:\n",
    "    v -- python dictionary containing the current velocity.\n",
    "                    v['dW' + str(l)] = velocity of dWl\n",
    "                    v['db' + str(l)] = velocity of dbl\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    \n",
    "    # Initialize velocity\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters['W'+str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters['b'+str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "v[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with momentum. The momentum update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta v_{dW^{[l]}} + (1 - \\beta) dW^{[l]} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha v_{dW^{[l]}}\n",
    "\\end{cases}\\tag{3}$$\n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{db^{[l]}} = \\beta v_{db^{[l]}} + (1 - \\beta) db^{[l]} \\\\\n",
    "b^{[l]} = b^{[l]} - \\alpha v_{db^{[l]}} \n",
    "\\end{cases}\\tag{4}$$\n",
    "\n",
    "where L is the number of layers, $\\beta$ is the momentum and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary.  Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$ (that's a \"one\" on the superscript). So you will need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_momentum\n",
    "\n",
    "def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using Momentum\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- python dictionary containing the current velocity:\n",
    "                    v['dW' + str(l)] = ...\n",
    "                    v['db' + str(l)] = ...\n",
    "    beta -- the momentum hyperparameter, scalar\n",
    "    learning_rate -- the learning rate, scalar\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- python dictionary containing your updated velocities\n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    \n",
    "    # Momentum update for each parameter\n",
    "    for l in range(L):\n",
    "        \n",
    "        ### START CODE HERE ### (approx. 4 lines)\n",
    "        # compute velocities\n",
    "        v[\"dW\" + str(l+1)] = beta * v[\"dW\"+str(l+1)] + (1-beta)*grads[\"dW\"+str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta * v[\"db\"+str(l+1)] + (1-beta)*grads[\"db\"+str(l+1)]\n",
    "        # update parameters\n",
    "        parameters[\"W\" + str(l+1)] -= learning_rate * v[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] -= learning_rate * v[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = [[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = [[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = [[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[0.02344157]\n",
      " [0.16598022]\n",
      " [0.07420442]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v = update_parameters_with_momentum_test_case()\n",
    "\n",
    "parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\"> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74493465]\n",
    " [-0.76027113]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]] </td> \n",
    "    </tr> \n",
    "\n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]</td> \n",
    "    </tr> \n",
    "</table>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Note** that:\n",
    "- The velocity is initialized with zeros. So the algorithm will take a few iterations to \"build up\" velocity and start to take bigger steps.\n",
    "- If $\\beta = 0$, then this just becomes standard gradient descent without momentum. \n",
    "\n",
    "**How do you choose $\\beta$?**\n",
    "\n",
    "- The larger the momentum $\\beta$ is, the smoother the update because the more we take the past gradients into account. But if $\\beta$ is too big, it could also smooth out the updates too much. \n",
    "- Common values for $\\beta$ range from 0.8 to 0.999. If you don't feel inclined to tune this, $\\beta = 0.9$ is often a reasonable default. \n",
    "- Tuning the optimal $\\beta$ for your model might need trying several values to see what works best in term of reducing the value of the cost function $J$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Momentum takes past gradients into account to smooth out the steps of gradient descent. It can be applied with batch gradient descent, mini-batch gradient descent or stochastic gradient descent.\n",
    "- You have to tune a momentum hyperparameter $\\beta$ and a learning rate $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Adam\n",
    "\n",
    "Adam is one of the most effective optimization algorithms for training neural networks. It combines ideas from RMSProp (described in lecture) and Momentum. \n",
    "\n",
    "**How does Adam work?**\n",
    "1. It calculates an exponentially weighted average of past gradients, and stores it in variables $v$ (before bias correction) and $v^{corrected}$ (with bias correction). \n",
    "2. It calculates an exponentially weighted average of the squares of the past gradients, and  stores it in variables $s$ (before bias correction) and $s^{corrected}$ (with bias correction). \n",
    "3. It updates parameters in a direction based on combining information from \"1\" and \"2\".\n",
    "\n",
    "The update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\n",
    "where:\n",
    "- t counts the number of steps taken of Adam \n",
    "- L is the number of layers\n",
    "- $\\beta_1$ and $\\beta_2$ are hyperparameters that control the two exponentially weighted averages. \n",
    "- $\\alpha$ is the learning rate\n",
    "- $\\varepsilon$ is a very small number to avoid dividing by zero\n",
    "\n",
    "As usual, we will store all parameters in the `parameters` dictionary  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Initialize the Adam variables $v, s$ which keep track of the past information.\n",
    "\n",
    "**Instruction**: The variables $v, s$ are python dictionaries that need to be initialized with arrays of zeros. Their keys are the same as for `grads`, that is:\n",
    "for $l = 1, ..., L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "s[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "s[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters['W'+str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters['b'+str(l+1)].shape)\n",
    "        s[\"dW\" + str(l+1)] = np.zeros(parameters['W'+str(l+1)].shape)\n",
    "        s[\"db\" + str(l+1)] = np.zeros(parameters['b'+str(l+1)].shape)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "v[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n",
      "s[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "s[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "s[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "s[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with Adam. Recall the general update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{W^{[l]}} = \\beta_1 v_{W^{[l]}} + (1 - \\beta_1) \\frac{\\partial J }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{W^{[l]}} = \\frac{v_{W^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{W^{[l]}} = \\beta_2 s_{W^{[l]}} + (1 - \\beta_2) (\\frac{\\partial J }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{W^{[l]}} = \\frac{s_{W^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{W^{[l]}}}{\\sqrt{s^{corrected}_{W^{[l]}}}+\\varepsilon}\n",
    "\\end{cases}$$\n",
    "\n",
    "\n",
    "**Note** that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate = 0.01,\n",
    "                                beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = beta1 * v[\"dW\"+str(l+1)] + (1-beta1)*grads['dW'+str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta1 * v[\"db\"+str(l+1)] + (1-beta1)*grads['db'+str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l+1)] = v[\"dW\" + str(l+1)] / (1 - beta1 ** t)\n",
    "        v_corrected[\"db\" + str(l+1)] = v[\"db\" + str(l+1)] / (1 - beta1 ** t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l+1)] = beta2 * s[\"dW\"+str(l+1)] + (1-beta2)*grads['dW'+str(l+1)] ** 2\n",
    "        s[\"db\" + str(l+1)] = beta2 * s[\"db\"+str(l+1)] + (1-beta2)*grads['db'+str(l+1)] ** 2\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l+1)] = s[\"dW\" + str(l+1)] / (1 - beta2 ** t)\n",
    "        s_corrected[\"db\" + str(l+1)] = s[\"db\" + str(l+1)] / (1 - beta2 ** t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] -= learning_rate * v_corrected['dW'+str(l+1)] / (np.sqrt(s_corrected['dW'+str(l+1)])+epsilon)\n",
    "        parameters[\"b\" + str(l+1)] -= learning_rate * v_corrected['db'+str(l+1)] / (np.sqrt(s_corrected['db'+str(l+1)])+epsilon)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63178673 -0.61919778 -0.53561312]\n",
      " [-1.08040999  0.85796626 -2.29409733]]\n",
      "b1 = [[ 1.75225313]\n",
      " [-0.75376553]]\n",
      "W2 = [[ 0.32648046 -0.25681174  1.46954931]\n",
      " [-2.05269934 -0.31497584 -0.37661299]\n",
      " [ 1.14121081 -1.09244991 -0.16498684]]\n",
      "b2 = [[-0.88529979]\n",
      " [ 0.03477238]\n",
      " [ 0.57537385]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[0.02344157]\n",
      " [0.16598022]\n",
      " [0.07420442]]\n",
      "s[\"dW1\"] = [[0.00121136 0.00131039 0.00081287]\n",
      " [0.0002525  0.00081154 0.00046748]]\n",
      "s[\"db1\"] = [[1.51020075e-05]\n",
      " [8.75664434e-04]]\n",
      "s[\"dW2\"] = [[7.17640232e-05 2.81276921e-04 4.78394595e-04]\n",
      " [1.57413361e-04 4.72206320e-04 7.14372576e-04]\n",
      " [4.50571368e-04 1.60392066e-07 1.24838242e-03]]\n",
      "s[\"db2\"] = [[5.49507194e-05]\n",
      " [2.75494327e-03]\n",
      " [5.50629536e-04]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v, s = update_parameters_with_adam_test_case()\n",
    "parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.75225313]\n",
    " [-0.75376553]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[  1.51020075e-05]\n",
    " [  8.75664434e-04]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
    " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
    " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]] </td> \n",
    "    </tr>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You now have three working optimization algorithms (mini-batch gradient descent, Momentum, Adam). Let's implement a model with each of these optimizers and observe the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Model with different optimization algorithms\n",
    "\n",
    "Lets use the following \"moons\" dataset to test the different optimization methods. (The dataset is named \"moons\" because the data from each of the two classes looks a bit like a crescent-shaped moon.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e141722358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already implemented a 3-layer neural network. You will train it with: \n",
    "- Mini-batch **Gradient Descent**: it will call your function:\n",
    "    - `update_parameters_with_gd()`\n",
    "- Mini-batch **Momentum**: it will call your functions:\n",
    "    - `initialize_velocity()` and `update_parameters_with_momentum()`\n",
    "- Mini-batch **Adam**: it will call your functions:\n",
    "    - `initialize_adam()` and `update_parameters_with_adam()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer, learning_rate = 0.0007, mini_batch_size = 64, beta = 0.9,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 10000, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 1\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "\n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            a3, caches = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost\n",
    "            cost = compute_cost(a3, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, caches)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('epochs (per 100)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate))\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will now run this 3 layer neural network with each of the 3 optimization methods.\n",
    "\n",
    "### 5.1 - Mini-batch Gradient descent\n",
    "\n",
    "Run the following code to see how the model does with mini-batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690736\n",
      "Cost after epoch 1000: 0.685273\n",
      "Cost after epoch 2000: 0.647072\n",
      "Cost after epoch 3000: 0.619525\n",
      "Cost after epoch 4000: 0.576584\n",
      "Cost after epoch 5000: 0.607243\n",
      "Cost after epoch 6000: 0.529403\n",
      "Cost after epoch 7000: 0.460768\n",
      "Cost after epoch 8000: 0.465586\n",
      "Cost after epoch 9000: 0.464518\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e14206aeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.7966666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e13f6f8eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"gd\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Gradient Descent optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y.reshape(train_Y.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.2 - Mini-batch gradient descent with momentum\n",
    "\n",
    "Run the following code to see how the model does with momentum. Because this example is relatively simple, the gains from using momemtum are small; but for more complex problems you might see bigger gains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690741\n",
      "Cost after epoch 1000: 0.685341\n",
      "Cost after epoch 2000: 0.647145\n",
      "Cost after epoch 3000: 0.619594\n",
      "Cost after epoch 4000: 0.576665\n",
      "Cost after epoch 5000: 0.607324\n",
      "Cost after epoch 6000: 0.529476\n",
      "Cost after epoch 7000: 0.460936\n",
      "Cost after epoch 8000: 0.465780\n",
      "Cost after epoch 9000: 0.464740\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e142154278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.7966666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1423a0a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = \"momentum\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Momentum optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y.reshape(train_Y.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.3 - Mini-batch with Adam mode\n",
    "\n",
    "Run the following code to see how the model does with Adam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690552\n",
      "Cost after epoch 1000: 0.185567\n",
      "Cost after epoch 2000: 0.150852\n",
      "Cost after epoch 3000: 0.074454\n",
      "Cost after epoch 4000: 0.125936\n",
      "Cost after epoch 5000: 0.104235\n",
      "Cost after epoch 6000: 0.100552\n",
      "Cost after epoch 7000: 0.031601\n",
      "Cost after epoch 8000: 0.111709\n",
      "Cost after epoch 9000: 0.197648\n"
     ]
    },
    {
     "data": {
      "image/png": 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i4gVuBa4GtgI3iMjWDMeFgT8FnirUWnLBsRS0qllRlGKmkJbCTqDdGHPIGBMDfgRcl+G4/wV8AYgUcC2zEtSRnIqiKAUVhWbgeNLlDvs6FxG5AGg1xvxipgcSkZtFZJeI7Oru7s7/SrHqFEAtBUVRiptCioJkuM64N4p4gC8DH5/tgYwxtxljdhhjdtTX1+dxiVPoSE5FUZTCikIH0Jp0uQU4kXQ5DJwLPCgiR4BXAXctVrDZcR9p/yNFUYqZQorCM8AmEVknIn7geuAu50ZjzKAxps4Y02aMaQOeBK41xuwq4JqyEnJiCmopKIpSxOQkCiLyzlyuS8YYEwduAe4BXgF+YozZIyKfE5Fr57PYQlLmZB+ppaAoShHjy/G4vwB+msN1KRhj7gbuTrvuM1mOvSLHtRQEv8+D3+tRS0FRlKJmRlEQkauBNwHNIvLVpJsqgBW3pQ7q9DVFUYqc2SyFE8Au4Frg2aTrh4GPFmpRi0VI5zQrilLkzCgKxpgXgBdE5AfGmAkAEanGqi3oPxMLPJME/WopKIpS3OSafXSviFSISA3wAnC7iPxdAde1KAQDPq1oVhSlqMlVFCqNMUPA24DbjTEXAVcWblmLQ0gtBUVRipxcRcEnIquBdwEztqRYzgT9XrUUFEUpanIVhc9h1RscNMY8IyLrgQOFW9biEPT71FJQFKWoyalOwRjzU5JqEowxh4C3F2pRi0Uo4NU6BUVRippcK5pbROROEekSkdMicoeItBR6cWeaoN+nFc2KohQ1ubqPbsfqW9SE1f76P+zrVhQhv5exiUkSCTP7wYqiKCuQXEWh3hhzuzEmbv99GyhMD+tFJBjwYQxE4upCUhSlOMlVFHpE5L0i4rX/3gv0FnJhi8HUSE4VBUVRipNcReH3sdJRTwEngXcAHyjUohaLqZkKKgqKohQnuXZJ/V/AjU5rC7uy+f9hicWKwRnJOappqYqiFCm5Wgrbk3sdGWP6gAsKs6TFo8yxFFQUFEUpUnIVBY/dCA9wLYVcrYxlQ0Wp9ZIGxiYWeSWKoiiLQ64n9i8Bj4vIzwCDFV/4fMFWtUg0V5cB0NE/vsgrURRFWRxyrWj+rojsAl4HCPA2Y8zLBV3ZIlBfHqC0xMPxvrHFXoqiKMqikLMLyBaBFScEyYgIrdVBjqkoKIpSpOQaUygaWmuCHFf3kaIoRYqKQhqt1WV09I1hjLa6UBSl+CioKIjIVSKyT0TaReRTGW7/IxF5UUR+KyKPisjWQq4nF1prggxH45qBpChKUVIwURARL3ArcDWwFbghw0n/B8aYbcaY84EvAIs+4rO1JgjA8f6puMJkwvCFX+3lWK/GGhRFWdkU0lLYCbQbYw4ZY2LAj4Drkg+wR3w6hLDSXReV1mpbFPqm4gr7Tg3ztQcP8qs9JxdrWYqiKGeEQhagNQPHky53AJekHyQi/w34GODHSnmdhojcDNwMsGbNmrwvNJnWGqtWIdlSeOnEIAA9I7GCPreiKMpiU0hLQTJcN80SMMbcaozZAHwS+J+ZHsgYc5sxZocxZkd9fWE7dodLS6gOlqSkpb58wjJoeoajBX1uRVGUxaaQotABtCZdbgFOzHD8j4DfK+B6cqa1JphSwPZSp2UpdI+oKCiKsrIppCg8A2wSkXUi4geux5re5iIim5IuXgMcKOB6cqa1Jui2ukgkDC+ftC0FdR8pirLCKVhMwRgTF5FbgHsAL/AtY8weEfkcsMsYcxdwi4hcCUwA/cCNhVrPXGitDvLrPaeYTBiO9I4yFpsk6PfSo5aCoigrnIJ2OjXG3A3cnXbdZ5L+/2eFfP750lpTxsSk4fRQhD12POGyDbXcv7eLyYTB68kULlEURVn+aEVzBtY4tQp9Y+zpHMTv9fCq9bUkDPSPqQtJUZSVi4pCBpxahWN9Y+w5McTmVeWsrrRSVdWFpCjKSkZFIQNNVWWIwPH+cV46Mci5TZXUlfsB6BlWS0FRlJWLikIG/D4PTZVlPHmol4GxCc5prqQuHADUUlAUZWWjopCFluoynjnSB8A5TRXUlasoKIqy8lFRyEJrTRBjwCNw9qoKKkp9+L0eLWBTFGVFo6KQBScDaUN9OWV+LyJCXblfYwqKoiyYyYThSM/oYi8jIyoKWXAa453bXOleV1seUPeRoigL5he7T3Dl3z20JM8nKgpZcNJSz2mqcK+rK/cvyQ9RUZYzTx3qXbK75kJxvG+MeMJwYmDpjf5VUcjCtpZK3nPJGq7Zvtq9rk4tBUXJOx/7yQv8w/3ti72MM0rvqOWGXornk4K2uVjOBHxePv/WbSnX1YUD9I7ESCQMHm11oSh5YWh8goEi6xTQ54jCEoxRqqUwB+rKA8QThsFxnd+sKPnAGMNoLF50vylHFJZiNqOKwhxwq5qX4AeprGy6V+iAp2g8QcLAUKS4RKF3ZOm6j1QU5kC9XcBWCHWPTyboH116pqSy+BzsHmHn/7mP5471L+o6BsZi/OjpY3l9zNFoHICh8XheH3ep47qPluCMFhWFOTDV6iL/H+R3nzjKa7/4AJGJybw/trK86ewfxxg42DWyqOu447lOPvXzF+nMY8bMWMz6vheT+8gYkxRTUEthWeO2ukj6IH+y6ziv2JPZFsLeU0MMReLu/AZFcRiOWLvoxfY/d9rTCPvyuCkajVmvbXxiklg8kbfHXcoMR+PEJq3Xqu6jZU5VWQlej7gfZP9ojE/esZtvPHJ4wY/t7L52dwws+LGUlcWw7W9f7EwVJ6c+nzNFRqNTlvFwkcQVHFENLdFpjioKc8DjEWpDUwVsj7b3YAwc6lm4We/swl44rqJQKEaicX78zDGMMYu9lDkxEl0alsLJwfyLwnhsShSKxYXk1ChsXhWmf2yCicmlZSGpKMwRq4DN+lAfOdANWL7ehZxoEgnDicEIAC90DC58kUpG/unBdj55x4vsXmbv8ZDtPlps/3PngPUdHRjL38nbcR/B1Otc6TjxhC2N4ZTLSwUVhTlSF7aqmo0xPLy/B69HGIrEXfWfDz2jUWLxBKsrSzncM8pgHn90isV4bJIfPGVlzhxeZi0VHLfKYloKkYnJKbdpHi2FsWRRKBJLoW/Ueh8326Kw1NKNVRTmiNUpNUp71winhiK8cWsjAIe653+icVxHV527CoDdnepCyjd3Pt9Jvy22R3qXmyjY7qNFPHmcsi1ZyLOlEC1e99GWVbYoLLG4QkFFQUSuEpF9ItIuIp/KcPvHRORlEdktIr8RkbWFXE8+qLfdRw/tt1xHN13WBsCh7vnHFZwg89XnWn2WNK6Qyr8938m9L5+e9/2NMXzrscOc01RBc1XZsmu+NmKLwuD4BNH44qQsJzduy6e7I8VSKKJAc9DvpaXanvueg9iPRuNc89VH+NVLJwu9vMKJgoh4gVuBq4GtwA0isjXtsOeBHcaY7cDPgC8Uaj35oq48QGwywX++eJIN9SEubqsh4PNwcCGiYFsKZ60Os6E+xG+PLy+fdyHpGo7wiTt28/WHDs77MR7a30171wgf/J11tNUFOdw7lscVFp7h6NTJsneRip2cjUt1sKRg2UfFUsDWNxqjJuRPmuY4+/vZOTDOnhNDRM9A2m4hLYWdQLsx5pAxJgb8CLgu+QBjzAPGGOcX+iTQUsD15IW6sNXq4vljA1y+qR6PR1hXF1qY+2hgnHCpj4rSEs5rqeKFjoFllyFTKL75yGFi8QRdC3CdfPPRwzSEA7x5exNttSGOLkP3kdN/cbFcSCdt99HZqyvy6j4ai8UpLfHg93qWnftoJBp3M8PmQs9ojNqQn1DAR1lJbmmpzsaxxW7pX0gKKQrNwPGkyx32ddn4IPDLTDeIyM0isktEdnV3d+dxiXPHUXeA126uB6zpbIcW4JI4MTBOc5VlSp7XWkX3cJRTQ5FZ7rXy6R+N8f0njwLWyXA+Qrn/9DCPHOjh/Zeuxe/z0FYbYmBseXXlHInEaXZcDYvkfz4xME5deYDGitL8WgqxScoDPirKfAt2Hz28v5s3/f0jKWmuheRPf/g8f/rD5+d8v77RKDUha3NZF85tRktHv7V3brW/B4WkkKKQqbd0xl+1iLwX2AF8MdPtxpjbjDE7jDE76uvr87jEueOIgt/r4ZL1NQCsrw9xrG9s3hWZHf3jrn/xvNYqYGnEFR5r7+G2h+fvtlkotz9+hNHYJG+7sJnxicl57coe2NsFwH+9eA0AbXUhIDUDyRjDf7xwYtH89bMxFImzvq4cWDxLoXNgnOaqUqqCJfm1FKJxgn4fFWUlC84+euJQLy+fHGLPiTPjfj3YPcKTh3qJz7HOoG8kRk3IOo/kOqOlo38cv9eTsiktFIUUhQ6gNelyC3Ai/SARuRL4NHCtMWZpheEz4HwoO9qqCfqtcRTr60NMJgzH+uZnLXQOjNNkWwpnrw5T4pUlEVe449kOvnLfgUV57uHIBN9+7DBv2NrI5ZvqAOblQjrcM0pduZ96u2/VujrL/D6aFFd48lAfH/7h866ALDWGIxOss8VsMS2FpqoyqoN+RqLxvLWkGI1NEvR7qSgtWbD7yHGxnKk6lO7hKGOxSfadHs75PsYYekdj1Nodl+vKAzlVqncMjNNcXXZG5rgUUhSeATaJyDoR8QPXA3clHyAiFwBfxxKEpfmLTKMm5Ke1pozrzm9yr9tQb+3iDmaJKzy8v5tf7zmV8bahyATDkbjrPgr4vJy9uiKjpfDKySF+/9vPnLETw1BkgrHYpNvJ8kzy/SePMRSJc8vvbqQhXApA19DcX/ehnlH3hAqWT1Yk1VLYdaQPWJodK2PxBNF4gtqQn4pSX94thVxccsYYTgxELFGw3R4D4/l5r8ZicUIB21JYYPGaEwx/sbPwojAajbvN/J47lrtVPxabJBpPTLmP5mApOOeIQlMwUTDGxIFbgHuAV4CfGGP2iMjnRORa+7AvAuXAT0XktyJyV5aHWzJ4PcIjn3id644A3JNOpgykWDzBx3/6Ap+4Y3fG3ZWzu2lO8hWe11LFi52DKel6nQPj3HT709y/t4vH2nvy9npmwskGWUiQd778+JljXLahlvNaq2iwd/ldw3OPsxxOE4XSEi9NlWUpweZdR62W1EuxdbnjMguX+qgLB/Ka0/7Zu/aw/a9/zQe//QzfeORQ1gD8wNgE4xOTtqVQAkD/aH5cSKNRy1KoLCthOE+WwpkQheTfxPNHc29p7qTzOqJQX+6nbyw2qwuqs3/MdTEXmoLWKRhj7jbGbDbGbDDGfN6+7jPGmLvs/19pjGk0xpxv/1078yMuTcKlJTSEAxkzkO7Zc4ru4SgDYxMZT+auKCTtAq7c2shoLM5b/uFR9pwYZHBsgpu+9TRj0Ul8HuGVk7mbqwvBMee7znDQOzIxydG+MXaus2I2jqUw0y7ZGDPthzUcmaB7OMo62x/vsK4u5KalJhLGnVPQvwQryZ1q5nBpiVUjk8emeE8e6iXk93G4Z5T//Z+vcOO3ns543Am751FTZSnVQetklq9g81gsTsjvo6J0YYHmWDzB6eEIZSVeDnaPzCv+NJdEBue7WFHqm9OcC6dwzRnYVRcOYAz0zfB+WtXksZUhCsXEhvryjAVs33viKC3VZVSU+viPF6aFVNwfXLKl8NrN9Xz/g5cwHInz1lsf5x3//DhHe8f4+vsvYmNDeV5adeeC8yNNtxT6R2Pct4Bistk43DOKMVNuuYoyH36fZ0ZR+PrDh7jy7x5K+WEf6bFO/MmWAkBbXdAtYDvQNeJWDC/FjCRnbeWlPurzaCkYYzjWN8abtq3m/v9+BX98xQaO949n3LGesHseNVWVUWVbCvl6r0ajkwQDXirKrJjCfFOxTw1GMAZ+96x6jIE9c7QWRqJxLvrf9/GL3dN/o5lwvotXnt3Ikd4xenP8XJwWF8mBZpi5A25HBm9CIVFRyBPr60Mc7B5N+VLvPTXE00f6eN+r1nLVuav49cunpw3R6ewfx+/zUBdKzSp49cY6fvWR1/CazXW0d4/wxXdu57INdWxtqjhzojCeWRR+8PQx/uC7u9w0uXzjuOEcURAR6ssDM7qx9p8a5kjvGMf7pipvne616+vTRKE2xKA9LH7XUSueUDXHoqw/+t6zfPPRhbdMnw1HFMKlPurKA3mLKXSVSlLPAAAgAElEQVSPWEHSNjvwvqYmyGTCZHyPnWpmJ9AM+bOqHEuhsqyEiUlDZGKeGXwD1nfxKrsrQLoL6XjfzN/VlzoH6RuN5TzPpNt2Zb7xHKs1zfM5xhWcuFVtUkzBuj775+rESs5EjQKoKOSN9fXlDI5PpLQA+N4TRwn4PLxrRytvOa+JkWicB/el1ll02DUKmbIKakJ+/uX9O9j16Su57nyrxGPr6gq6hqMFDzbHJxOM2oG0dF++s3N5xg7Q5puDXaOIpJ7MGyoCM8YUeuz3PflkcLjHepw1Nak/prbaqbTUZ4/2Uxvys625kr4cT3STCcN9r5zmwX255UYMjMX49J0v8t/+9TkSibnthB33UUVpCfXhACPReF7y8J3sq7X2e+Fkv53IMFXtxIC1cakN+fPuPhqN2ZZCqWWBzNeF5Fgz25sraaosTclA+uWLJ7n8Cw/M+Hm9aB9/OkdXaddwFJ9HeM3mOnweydmFlB5TyGXuu7P5WvaB5mJjg30Cc4rYhiIT3Pl8J285r4nqkJ9L19dSG/LzH2nmaecsWQUiQm1SbvLZqysACm4tJGeCdKdl/TgnjqcPF2Zm8MHuEVqqyygt8brXNYQDM2YfOWZ5uig0VaY+DkzVKhzptUThorXV1IT8ObtETg6OE0+YWavYjTHc+XwHr//SQ/zrU8f4zxdP8suXMmehZcPxjZcHfG5abT42BI77bK0tmM1VVtwm06jNzoFxmipL8XiEMr+XgM+Tl1qFickEsXjCiimUWend801LdWJzq6tK2dZSmfI9uP3xIwD8/W8OZHVPOcfnaol1D0epKw8Q9PvY2lQxJ1EI+DwE/dZ3si6Hz7SjfxyfR2isKM3pORaKikKecFwdh7qt2Qo/fOoYY7FJ3vcqq8efz+vh6m2ruP+VrmlZRU1VuX/YZ0wUkn6c6S4FRxR2FcpS6B5x30+HhnDpjO4jZ5rVS2mikO46AmitKcMjsOtIP0d7x9jRVk110J9z9pHjojoxOD7jTO0v37ufj/74BVprgvziw7/D5sZyvnTvvjkVOyW7j+rLnSyshYvC0d4xvB5x/dSrKx1LYfpO+cTAuHs7MKf3aiaclE4n+wjm3z67c2CMhnCAgM/L9pYqqwX9+AT7Tg3z9OE+tq6u4PljAzzW3pvx/o4o5GopdI9EaaiwPo8LWqvY3TGY0+faO2K1uBCxPAPhgBUvmykdurPfqhHxnoEaBVBRyBtNVWX4fR6+ct8BzvvrX/M3v9zLBWuq3AplgLdsb2J8YpL7XrHM2MjEJN3DUZqrcvcV1oT8NFYECp6B5Jjxfm9qgNfKWR+nxCsc6BrJexpnwt6Bp4tCfTiQtUuoMSbFfWSMwRjD4e7RaUFmsGpBmqrK3MD/RWtrqApaefK5/LAd/7QxqUVw6dy/r4uL26r5+R9fxrnNlXzsDVs41D3Knc93zvocDo77yAk0Q34shaN9Vopjidc6BYQCll8/k/vo5GDEdS8BVIf8eYkpOJujUMC3YPdRcgHotuZKwAo2f+/JI/h9Hm7/wMU0VgT4h/unF2MORSY43DOKR3IX3K6hqCvSF66tzrmIrW80So3tMoKpeNlMnVI7+sfOmOsIVBTyhtcjvGV7E9VBP9dsX83fvG0b37rx4pRjLm6robEiwB3PdmCMcXvUzzWrYOvqwgebnRqFtrpgii9/aDzOaGySK7Y0APOLK3QNRbL61k8MjjM+MZnBUrB+gJnM+9GYNfS9rTbI4PgEx/vG6RmJMRyNZxQFsDKShiJx/D4P5zZXuD7egRx2qseTAuyHs4xinUwYDpwe4byWKjde9F/OaWR7SyVfue9Azi01hqPWGgM+rysK+Qg2H+0ddeMJDk1VZdNEYWIywemhiOtegvx1SnU6pAb9VvYRpLqPfv5cBz9+5lhOj9XZP+7+jhxRePxgL3c+18lbtjfRWFHKH75mA08d7uPpw6nfWce6vGhtNQNjEzNafw7dI1H387hwTTWQWxGb1SE1NalktvqT5DY4ZwIVhTzypXedx91/djl/87bt3LBzjVv96eDxCO+/tI2H9nfz2bv2TKWazXEXcPbqCtq7RnI6sfSORJmcY3ATpnZsmxqsObJO4d3U7IdV+L0et/ArVwbHJ7j8Cw/ws2c7Mt7uVIVvSHP7OKZ6pp2c4zpyGhS+2DnoVixnE4W1tZZ1tr25koDPS5UdQM0lrnCsb8zNHslWxX60d5RoPOEOUgFrV/jf37iFzoFxfvzM8Yz3S2c4Eqei1PK3O8K1UEvBGMPhnlE3nuDQXFU6LaZweihCwpBqKQT9eREF11Kws48gtX32bQ8f4vbHjsz6OImEVXHdYq+x2u468I1HDzEam+T9l1ou3Bt2rqGu3D/NWnCCzK8/2xqYlS66juXpMJkw9I5E3Y1KS3UZdeWBnIrYeu0OqcnUl/uzuo+i8Um6hqNnLB0VVBTOOH9yxQY+dPk6vvPEUT79by8CzHkXcPbqCuIJQ3vXzDMcuoYjXPHFB/n9bz8zZ2FwdmwbGuxGbPaJyBnevq4uxHmtldN2XbNxcnCcaDzhpoKmc9B+Tc7zOszU6qLHDjJfuqGOEq+wu3PA3cGvTytcc3AykC5qs3Z5bqVuDm6R431jbFkVpiEcyDrac98py5WQLAoAl2+qY+e6Gv7x/vacMpGGI3HCtmulxOuhJuRfsKUwMGa1VnGE0SGTpZBco+CQr6Z4rqUQ8BK2hc+JKSQShiO9ozmNue0ZiRKbTKScOLc3VxGZSLC9pdJ14Zb5vXzo8vU8cqCH3ya1kXmxc5DmqjLOsj+r9Cy3N331Ub76m3b3cu9olITBtRREhPNbK3NKZ+3LIAoztbpw3v8zlY4KKgpnHBHhf7zpbP7s9Zs42juGR2BV5dyyCqaCzTP7ML/2wEFGYnEe2t/NF+7ZO6fncH6cG+2Ts1PV7Jw0mqvK2NFWw0tp7ThmwzmhvZzF/XWwe4TKspLpuynXdTI9EOhYCqsrS9myKsxLnYMc6hmlxCtZd1iOe2rHWqtq2km1zGWq2LG+cVqrg1ZldDZROD2MiGVpJSMivO2CZrqGoxybJXceYCQyQXnA516uK1+4KDjjSNsyuI+GInE3jgGpNQoO1UErU2uu6bXpJFsKJV4rI8fZjJwcihCZSNA3OvvzdAxMt7i3tVgupPe+KnWY43tetZZwwMe3kmpMXuwcZFtzpZvdczpp4zEem+SVk0M8eWgqQO28/853Eqz3x9kwZWM8NslYbDIlpgCWKDivMz6ZSGmXMzVHQS2FFY2I8NE3bOazb9nKu3a0usG+XFlXF6K0xDNjXKGjf4x/feoo11/cynsuWcPXHzrEv/829wDnUGQCr0dYZ584HLdN50CEEq9QVx5gZ1sN8YRJ2XXNhrPT3396hIkMQd2D3SNsbCh3szMcrIyNzP705Nzvbc1VvNQ5xKFuy2eeLWPjNZvr+eoNF/D6s6zYSK6VuuMxa4D9mtog6+tnEIVTw7TVhijze6fddq4TCM1hZ2lZClOiUB/OrYHaTDhi5BSuOTgn/pNJ85idoHpyhlxVsISEmcqMyoXJhOG/fv0JHkiqFXDqYEIB6z2qLCtx3ZaHbbfcZMLMmqaaqX/Y753fzIcuX8e15zWlHFse8PHOHa3c/eJJTg9FGByb4GjvGNtaKl13UHIGkvNeHeia2oBlEoXGilKGIvEZN0i9tkU73VLwM5kw/NVde7j0/97P67/0EL980Rq7eaZrFEBFYVG56dXr+L9v3z7n+3k9wpbGMC/PcFL56m8OICJ8+HWb+Ku3nMPOtho+ecduvnjPXj5954v84fd2cefzmf36YPl2K0p903z5JwbGWWXnrF+4thoReGYO9QqOGyoWT2TM8z/YPTotngBWSm9tKHNVs+NiqC23itAGxyd48lBv1ngCWO/htec1uUFgx18/m/vICTK3VJexri5E32gso5DsOz3M5sbMrqtNjeX4PMJLOfT9nyYK5QtvdXGkZwyR6S6JTLUKe04M0VYbdNvEA/MqYOsajvDU4b6UHfeYXYPhPHZFaYkbUziUFMB3TqbZ6MxgKayqLOXT12ydVqMC1lz1SWP4/pNH3c9gW3Ml1UE/JV5J+Y45TQJ7RmLu5sMRBcelCbDKtjJODWZPaZ3avKQGmlfZ6b4/fPoY57VUsaYm6NZUdPSP4/UIq+foTVgIKgrLlK1NFbxyaihjMc7B7hF+9mwH771krZsq+7X3XkhTVRm3PnCQX750iqcP9/GZf9+TNQVwcHzCdeOIQHeS+6jJ/hJXlpWwpTGcNT6QieSYQLqlMzhuNbBLzzxyaAhnEYWRKGUlXoJ+n5t5MhyJs34GUUinrMSL3+eZ9UTn7JzX1ATdRnvp1kJkYpIjPaNsWVWR8TECPi+bG8MpNRXZGInGKQ+UuJedVhcLGdd6tHeU1RWl006YmaqaX+wcdC0bh+qQE3/JXRQc6yO5x49rKTiiUOZzrYLkDcNsLc07+8epKPW5sZfZWFMb5PVnNfKDp46x64i1odnWXInHIzSESzNaCmBN8YOpDVLywBvnpD3TxMTetGpmh9ef3cA/v/dCnvofr+cbN+7gz16/ib2nhvnNK110DoyzqqIU3xy9CQtBRWGZ4szKzfQl/PK9+ykt8fInv7vBva6uPMC9H30tBz5/Nc/95Rv4nt1w77t2tWc6Q5EJKspK3B26sztNHh0KsHNdDc8d7c+5IKt7JEqzLVTpcYVDaT2P0snW6sIZhA6weVU5fvsH1DYHURARK9VylpiCc5JorQm6lki6KLR3jZAwsKUxPO3+Duc2V/DyicyinsxQZGKa+ygyMdWCZD4cyZCOCtbO1+sRVxR6R6J0DoyzvSVNFOZhKTg76GQrx7EUHBdbRemU++hQzyhltmj1ziYKA+M0zzEQ+4FXt9E7GuMbjx6ipXpqTkR9OLW/1LG+MdcFecAWhe7hKOGAL8U12FjpxCNmsBTS+h45lHg9XHXuardzwbXnN9FaU8Y/PNDO8b6xM5p5BCoKy5atdrA52RwHa/f9i90n+cCr26aN7vN6xI1fnNtcyevOauCbjx7OOERnaHzCLShyWkzEJxOcGkotZLpwTTWjsUnaM3SIzUT3cISmqtKM7i83HbUhsyjUl2dudZE8ySrg87oZPzO5jzJhpVrO4j7qGyfo91Ib8rOmJohHpotCtsyjZM5pqqR3NDbjzjKRMIxEp1JSgbzUKhztHZsWTwDr+7GqotTNeHGqfLc1V6Uc54rCHGYqTFkKU+sejU3i93rw+6zvZEpMoWeEC9ZYzztbDGW2VjGZuGxDLZsbyxmOxF3rEqCxIpByYj/aO8aWxjDhgI/9p63vePdIlPqKNBeQ6z7KvlZHENMDzemUeD388Ws38sLxAZ4/PnBGg8ygorBsuWBNNZsby/mH+9tTdulfvnc/4YCPmy/fMMO9LT78uo30j03w/SePTrttKBJ3+9FYO/QoXcPRaTnrm+3dsPODmY2uYavo5+zVYV45mbpTbu8aocQrWYeTN1RYQdb09Nre0WjK7stxd8zFfQRTWTUzcaxvjNbqICKC3+ehtSbo9rty2H96GL/PQ1tt9t3ruc2WqO/pzB4XGpuYxBirmtnBEfr5isJwZILe0RhrajK/N81VZVMTzOz8fWetDvOzFKzHTD7Bj8XiBANTu21rTnOcyMQkHf3jXLjGilnN1pb6xMDci7tEhJsuWwdMZSqBFTBOzj463mcJ6MbGctd91J1UzewQCvgIB3wzWgpPHeqlrTbobrZm4u0XNbOqopTJhHHrL84UKgrLFK9H+PgbrbYJdzxnBYxf7Bjk1y+f5oOXr6MyOPsX74I11Vy+qY5/eeTQtM6byZaC1bY6kpSeOBX0Wl8fwiNTpvVsdA9HaQiXsnV1Bb2jsZQYwcHuEdpqQ1n9pw3hUhJmetpo8iB0gHfvXMMfvmZ9SnZILlSHSma1FDr6x2hNKvpaVxdyM2Uc9p4aZmN9+Yx+4LNXVyDCjMHm5AE7Dgu1FJy2HNkEq6mq1P2cd3cOsr4+NM1XHy714RHmVKvgWAq9SSmmo9FJN54AuIN2jvRa8zQ2NZZTE/S7LUwyMTg+wXA0Pq/snLdd2MyNl65NyVBqsNupRCYmmUwYjvePsaYmxOaGMAe6kiyFDN+txsrSrIHmyMQkTxzqdQssZyPg8/KHr10PnLk5Cg4qCsuYN25t5PzWKr5y3wEiE5N8+b79VJaV8Pu/sy7nx/jw6zbRMxLjB0+nthNwAs3g7NBjbuZN8g+wtMRLW23I3UXNRGRikuFInPpwgK1N1u4sOa5wsGvErYvIRKaxnOmD0MHa+f3Fm86eltY6G1WzNHpzBtO01ky9fqdWIdni2X96eEbXEVgZN+vrQrw0g6WQ3AzPwWkDnmmgUy6kt8xOp6mqjFODESYThpfs/P10PB6x3qt5xBQmE8ZtJTIWi7vdQsGyFIzBbXu9ri5Ebbl/RkshUzpqrpSWePnr685NycJqqJia8ndycJyJScOamiCbV4XpG43RMxKlezizKKyqKM3qDnzmSB+RiYTbHiYXbti5ho9cuYk3bl01x1e2MFQUljEiwieu2sLJwQifvGM39+/t4ubXrM/JPHXYua6G81oqUyZORSas4eJOP5qGcKl9krBOYKvTdmWbGss5kIP7yM3vLg9w1mrrpOnEFZ492sehnlF2tNVkvX+mVhfOIPT04N18qA6WMDDD9K++0RhjscmU+Qzr60KMT0y6LofBsQlODkZmFQWw3Fwv52ApJBevhQI+1tQE2Xtqfg0RncK19Gpmh6aqMuIJw8snhjg5GMkoCjD3quZTQxECduzAcSFZsxSSLAX7+/aCXfeyri5EbSgwY6A5UzrqQnAK2LqGI25SwdraoJte/MLxAUai8ZR01OT7ZnMfPbSvG7/PwyXrs3+/0ykt8fKRKzdPa5dTaFQUljmXbajj8k11/PtvT1AT8nPTZW1zfozNjeGUNERnh+oEOJ0d+m+PD1BR6ks5STn3P9I7OmsvJudkXl8RoKK0hNaaMtdS+NKv91NXHuCGna1Z719fbu/ikny+zgkjPc1vPlQHrSKioSxFWW7mUdLOcr3TMt3Oq9/fNXuQ2eGcpgpODEayVlFPWQqpIr9lVZi9p+bXEPFo7yh15QFCaZ+hg3NyvWePNfdhe0tVxuPm0v8okTCcHoqwtcmKTTjB5rFonFCypWC/zt8eH6A+HCBcWkJdODBjq4tOx3rNk4tlqoAtyrHeqfRjJ3b2qD1nPaOlUGnF3jK1lHlofzeXrKtJqfdYqqgorAD+/L9swSNWX6VsP/aZaKoqo2s46ja9czJAKpLcR2B1k2zKsCPb1BgmYZh16IzTosIJ0p29yur2+vjBHh4/2MufXLFhxh/NlKUwtRtzq0RnyejIhamsmswnoeO2q2JNbWpMAaYykJwd/EzpqA7nNjmVzZmthXRxdjhrVZgjvWM5dfNMZ9/pkRkD4M7n+6s9pxCxhCsT1cGSnFqCgBVHmJg0rtXRnWwpJH3ejrty76lhN0mgNuSfMfvocM8oITsbLB9MtbqIcLRvDJ9dONYQDlBR6uNxex5DNvfRZMJMW2/nwDgHukZyjicsNgUVBRG5SkT2iUi7iHwqw+2vEZHnRCQuIu8o5FpWMttbqnj0k6/jg3OIJSTTXFWGMVN+X6eAKNl9BBCNJzKa6Y5pPVtcwa0EtU/uW5sqONwzyv/95V5WVZTy7kvWzHj/0hKrcVpykDVbleh8mK0o63gGS2FVRSmlJR4ea+/hgb1dPLy/m3CpL6cK1HNsUcgWV5jJUpjMoSFiOq+cHOKF4wO8YWtj1mNW20kE7V0jbKwvz7rJsDK1cnMfOd8rJyvMKUYbi8XdFheAm+02mTDucKS6cj/DkXhWK3TPiSG2NlXMOX6UjepgiVvVfMyeOeHzehARNjeG3ZkJDRktBeu3kR5sfsgewXvFliIXBRHxArcCVwNbgRtEZGvaYceAm4AfFGodxUJTVdm8fxiO6e34Z51meG72UVrjr3TW1Vk9hmaLK3QNR/EI1Non8LNXV7iBxVtetzFjS4J00quae7MUBM2HqfbZmU92x/vGqCsPpBQteTzCWasquPvFU3zg289w78un2d5SmdNnURksoaW6LKulMBKdGrCTjNPNc19aXKFvNDZjEeF3Hj9CaYmH/3pxdhddRWkJYVsIssUTwBm0k/v4UmfdJV5xRX00mmopJMfCnO62TkFXJqskkTC8cnLIFdd8IDJV1Xysd4w1SQH5TUnWXzZLAaZXNT+0v4vmqrKsRZlLjUI6uHYC7caYQwAi8iPgOuBl5wBjzBH7ttznEyp5J729geNTr7R3bqUlXjtdMJ5RFAI+L221wZwshdrygFsh6hTgtVSX8a4d2U9UyTSEUzM8kvseLZSaWfLvj/WNsaZm+uv/1k0Xp7RDmEvR3LlN2VsuD0fieIQUvztY3U39Pk/KpK+xWJwrvvgAN13WxsfeuGXaY/WPxrjz+U7edmGzK37ZaKoqY9/p4ZT8/XSqgiVE4wnGY5MZm/4l43xeqypLqQ1NNfQbi6XGFJLTqNcluY/Aao+RPBIUrKD5aGzS/R7li4YKq0jyaO8o57VOvQeORez1iPtdSaaxcnpDvYnJBI+19/KW85ryZs0UmkK6j5qB5EkiHfZ1c0ZEbhaRXSKyq7u7Oy+LU6ZwXB0nslgKMJWql22e9KakPO5sdA+nFv20VJdxzbbV/PW157hVrbOxubGcvSeH3R1x32iU0hJPXgJ4mdpn/3TXcb5y336++psD7Ds1nFKj4FAT8nN+a5X75/jGc2FbSyWHe0Z56tD02cHDkTjlAd+0k4nP62FjfXlKBtITB3sZisT58a7jGQOdP951nGg8wY05JCI4n3F6e4tk5lLAdnIwgs8j1IUC1IWtGEEiYRhLyz4q9/twXqrjPnIshZ4MTfEcMd2aJe4xXxrCAQ50DTMUibM2qcjPCTbXlfvdRorJ1IUC+DyS4j567mg/I9H4snEdQWFFIZMszquLlzHmNmPMDmPMjvr65fPmLhdKS7zUlfs5MehYCqkxBZjyoWayFMA6WR/tHZ0x+Nk1PDXsHCxT/db3XOhOvMqFC9dWMz4x6Z4QrUlWC48nwPSirON9Y/z5z3bzlfsO8Hf37qd3NDZjyux8ePfONWyoD/EH39k1zY2UPGAnnbNWhdmXlIH0oO23Pj0U5ZEDqRun+GSC7z1xlEvX13JWliZ9yTRXl+ER2Lo6uyg4ldW5DLo/NRihscLqrOsMlInEnWZ4qa64cMCHzyOu+NbZFmCmtNQ9J4Yo8Yp7ss4XyVXNyUkFm2xLIVtRpNVQL5BiyT60vxufR7hsQ21e11hICikKHUCyT6AFOJHlWGWRaaoqo3NgKtDs93lSfPyziUIuGUjplsJ8cObhPn/M6m7ZOxLLi+sIphdlPX7QSj+85yOv4eD/eRMHPn8170sb2rJQqkN+vvfBSwiX+rjxW0+n9FEaTmuGl8yWVWFOD0UZGIthjOGBfV28dnM91cESfpo26vS+V07TOTCek5UA8Ae/s55b333hjG4hZyefbRxpMicHx11rtK48QM9wLGnqWurrqwyWsKYm6PbociyFTAVse04MsqkhnLOVmStOBhKQUpNSXx6gKlgy43e4sTK1VuGx9h7Ob63KuYPrUqCQovAMsElE1omIH7geuKuAz6csgKbKsiT3UXxaAZzTgrsxyy7J2a0lDyNJJmGn6s219UQ6LdVl1IcD7pD05A6p+aA6qSjr8YO91IcDbG4sT2kmmG+aqsr47gcvIWHgfd98ym1QmD5LIRmnDmLvqWEOdo/S0T/OG7Y2ct35zdy75zSD9muITyb454cO0VxVxpVn51ZN21YX4uptq2c8Zm1NkBKvZP28kzk1GHGnC9aHA/SORt3XmB4vaakKprTqDvm9lJZ4ptUqGGMV2GVLmV0Iyd/RZFEQET511VkziuuqitKULL4XOwe5bGNd3tdYSAomCsaYOHALcA/wCvATY8weEfmciFwLICIXi0gH8E7g6yKyp1DrUWbGmc9rjLHbZqeejD50+Xp+dPOrsvbzWVcXwueRrMHm/rEY8YTJmMo3F0SEC9dU8aw9JL0vj+4jsHzlfaPW7vvxg71ctqH2jAQINzaU8/fXn09H/zj3vXIacGYpZBYFxw2079QwD9rTzK7YUs87LmohNpngLrtC/Qv37OO3xwf4+Bs357Unv8/rYX1dOe2zZJwZYzg5GEmxFCYmjeuqTI8Fff39F/E3b9vmXhaRlOC0w+mhKL2jsYKIgmMp1JX7p6XkXr9zzYytKpJdT08e6iVh4NXLyHUEhc0+whhzN3B32nWfSfr/M1huJWWRaaoqZSw2yeD4REozPIfqkH/Gcnu/z0NbXShrt1SnYKk+Q3uAuXLhmmru2XOanpEoPSPRvLmPwEpL7egfo71rhO7h6Bn1Bb96Qx2rKkr5z90nue78ZoYjE1kzmRorAlSWlbD31DDH+8bY1FBOS3WQ5irDWavC/OzZDipKfdz28CHef+la3nZh/n9mGxvLZx0UNDA2QTSecHP4nRiBUy2cXKcAZGzRUlfunxZTcOIv58yQNjtfGu2415oMSQWzsaqylJGoNef68fYeykq8XGC7PJcLWtGsAFPtDToHxi1RmEMGjcPmxnK3W+rAWIx7Xz7tZsI4cxAaKha+q79wrfUje6y9h2g8URD30eMHrWygyzacOdPf4xGuOncVD+7vZjgyMaP7SETYsirM88f6efpwn5vdIiK8c0crLxwf4M9/tpuL26r5n9eklwflh00N5Rzrm7my2gm6OpaC448/aqfw5pI1VlsemDaSc8+JIUSsWpd84xRrZmsaOBOrk4btPHawl4vX1eQ95lFoltdqlYIxVasQYSgSn1NapcOmhjBH+8b4+E9e4JL/8xs+9N1d/Nxu653cDG+hbGuuxOcR7n3ZcrPkUxRq7G4N1nwAAA8VSURBVKKsx9p7aKkuy5iCWkjevH01sXiC+/d2MRyNTytcS+asVWH2nhomNpnaffO685vw2bn0X3vPRQU7KW1sKMcYq+V5Nhz/uhNTqLPdh87s43RLIRO1IX/KGE+wLIW22lBW99pCqA6WsLqylPNbM/d9mgnH9bS7Y5D2rpFl5zqCAruPlOVDcgGb5T6a+1fDqVD+5UsneftFLTy8v5ufP9fJO3e0TjXDW2BMAawU2nOaK932AXV5dh9F4wkea+/hzdubZr9DnrlwTTWrKkr5+XOdxOKJGTveOsHmkN/LjrYpF0VdeYBvf2CnG5QvFJsarOdv7xrJWlXszFFIjinAVAvv0BwsBWOMG9/Zc2KI8+Zx0s4FEeGRT/yuW2Q5F5yq5juf7wTg1cssyAwqCopNbciP3+ex3EeR+bmP3rC1kW9/4GIuWltNuLSEv7/vAF/5zX46B8bpHo4S8nvn1bAvExeuqXJbLOej75FDtV1VOxqb5LKNZ36X5/EIV29bxbft2dnZ3Ecw1e7iso11BHypO+7f2VT4k1FbXXDW9ianBsfxyJSFWFVWgtcjbkwhOEs1NFiiPzFpXAt2cGyCjv7xWXtlLYT5BuUdi+jR9h6qgiV5r7Y+E6j7SAGsk1FTZSmHukeYmDRzmsng4PUIV2xpcHOy33pBM8bAvz3fSfdI1K2KzgcXJgXv8tUhE0hpAXHp+sUx/a/ZthpnpMNM7pGzVlWwqqKUt14wr0YBCybg87K2NjhjWurJwQgN4VL3JOvxCLUhP8NOSmoOm4Rat4DNsjadduv57HmUL0pLvFTaw4IuXV+bsfJ5qaOioLg0VZXxyknrBz6fmEI6a2qDXNxWzZ3Pd9I1FMlLPMHBCTZDfvoeOTjxiY0N5XkVsbnguJBgeofUZEIBH0/+j9fzpllqCgrJpobyGdubnBqaqlFwcFxIHsEdvDMTzvFOrYKbeVSAdNR84Hx2y60+wUFFQXFpShranl6nMF/eekEL7V0j1uCUPGQeOTRVltJYEchb3yMHx320mG0JHBcSzOw+WgpsaghztHfMncWRTnKNgoMTbA75p/d1yoRTh9I7YsUVfvXSKdbUBF2xWGo02q93OQaZQUVBSSK5hcV83EeZuGbbavw+D9F4Iq+WgohwybrarG035ktrTZDLNtTy9gLk9c+FG3au4axV4RlnVi8FNjaUM5kw7pjPEwPjXPWVh/nzn77A04f73L5HyTiJAcEcMo+Sj+8ZifHEoV52He3nDy6f3+yQM8FZq8JsqA/NqVvuUmJpb0OUM0pzUgfU+QSaM1EZLOHKsxu4+8VTec+E+ey157hzjPNFaYmXH3zoVXl9zPmwuTHMrz7ymsVexqw4onXg9AibG8N87cF22rtGON435vZgSrcUnM1BLplHgFs02TsS4xe7T9AQDuTcan0x+MR/2cJHrty0bFplp6OioLikWgr5+2q87YIW7n7x1LQd40KpCfnzWqOgzJ0N9eWIWD2vTg9V85NnOnjnjlb+8s1nc8+eU9y/t5sr0ya9OW6fXC2FEq+HqmAJ9+w5xcsnh/jLN2/NaSDTYuHzevLaUuRMo6KguCSLQj4CzQ6/e1YDf/O2bVx17qq8PaayNCjze2mtDnKga4TbHj7EpDH88WutWdtvvaCFt14w3Q3nWIxziQXVhvy8fHKIunI/795ZuFRURUVBSSJ5/nI+W/16PcIN+kNesWxqKOf5o/30jcW47vymlBkEmahz3Ue57/ZrywMc7B7lQ5evn3XSm7Iwlq+No+Sd0hIvtSE/ZSXeZdevRVk8NjaWc2IwQjSe4E+u2Djr8XVhJ9Cc+560uaqMmpCf9+Z5noUyHbUUlBSaqsroGp59mpaiOGy0B9Jfs211TtlS87EUPn3N2Xz0ys15q4hXsqPvsJLCpoZyfN7lmTWhLA6vWl/L1tUVfOTKTTkdXx3045G5xRTqygOwtLNzVwxizLzGJi8aO3bsMLt27VrsZaxYhiITxOKJJVsYpKwMbn/sMBe31aRMWVMKi4g8a4zZMdtxaikoKeSraE1RZuIDr166xWfFjkYTFUVRFBcVBUVRFMVFRUFRFEVxKagoiMhVIrJPRNpF5FMZbg+IyI/t258SkbZCrkdRFEWZmYKJgoh4gVuBq4GtwA0ikj5B/INAvzFmI/Bl4G8LtR5FURRldgppKewE2o0xh4wxMeBHwHVpx1wHfMf+/8+A18tybS2oKIqyAiikKDQDx5Mud9jXZTzGGBMHBoHlOZlCURRlBVBIUci040+vlMvlGETkZhHZJSK7uru787I4RVEUZTqFLF7rAJInYbQAJ7Ic0yEiPqAS6Et/IGPMbcBtACLSLSJH57mmOqBnnvddzhTj6y7G1wzF+bqL8TXD3F93Tt0ECykKzwCbRGQd0AlcD7w77Zi7gBuBJ4B3APebWfpuGGPq57sgEdmVS5n3SqMYX3cxvmYoztddjK8ZCve6CyYKxpi4iNwC3AN4gW8ZY/aIyOeAXcaYu4BvAt8TkXYsC+H6Qq1HURRFmZ2C9j4yxtwN3J123WeS/h8B3lnINSiKoii5U2wVzbct9gIWiWJ83cX4mqE4X3cxvmYo0Otedq2zFUVRlMJRbJaCoiiKMgMqCoqiKIpL0YjCbM35VgIi0ioiD4jIKyKyR0T+zL6+RkTuFZED9r/Vi73WfCMiXhF5XkR+YV9eZzdZPGA3XfQv9hrzjYhUicjPRGSv/ZlfWiSf9Uft7/dLIvJDESldaZ+3iHxLRLpE5KWk6zJ+tmLxVfvctltELlzIcxeFKOTYnG8lEAc+bow5G3gV8N/s1/kp4DfGmE3Ab+zLK40/A15Juvy3wJft19yP1XxxpfH3wK+MMWcB52G9/hX9WYtIM/CnwA5jzLlY6e7Xs/I+728DV6Vdl+2zvRrYZP/dDPzTQp64KESB3JrzLXuMMSeNMc/Z/x/GOkk0k9p48DvA7y3OCguDiLQA1wDfsC8L8DqsJouwMl9zBfAarFofjDExY8wAK/yztvEBZXYXhCBwkhX2eRtjHmZ6d4dsn+11wHeNxZNAlYisnu9zF4so5NKcb0Vhz6a4AHgKaDTGnARLOICGxVtZQfgK8AkgYV+uBQbsJouwMj/v9UA3cLvtNvuGiIRY4Z+1MaYT+H/AMSwxGASeZeV/3pD9s83r+a1YRCGnxnsrBREpB+4APmKMGVrs9RQSEXkz0GWMeTb56gyHrrTP2wdcCPyTMeYCYJQV5irKhO1Hvw5YBzQBISz3STor7fOeibx+34tFFHJpzrciEJESLEH4V2PMz+2rTzvmpP1v12KtrwC8GrhWRI5guQVfh2U5VNnuBViZn3cH0GGMecq+/DMskVjJnzXAlcBhY0y3+f/t3W2IFVUcx/Hvz0JrUzaMiihKTawQzApFsmhDKIggA6UlrZCKCgsKotiKnsiIyiIoUTDQyh5MfMgSDC3UXojWalTKlijlvigKZMHKp/XXi3Pm7nW9d1dXc5/+nze6Z++dOfeOzn/mzMzv2AeBpcC19P3tDdW37Undv/WXolAK58t3JdSTwvj6lDyW/i6w3fYbZb8qggfJf6441X37v9husH2R7WGk7fqV7WnA16SQRehjnxnA9u/AbkmX5aZJwDb68LbOfgMmSKrJ/96Lz92nt3dWbdt+Btyd70KaALQUw0xd0W+eaJZ0C+kIsgjnm9XNXTrpJF0HbAB+oG18/SnSdYXFwMWk/1RTbR8VUd7bSaoDHrd9q6QRpDOHocAWYLrt/d3Zv5NN0ljSxfWBwE5gBulAr09va0kvAHeQ7rbbAtxHGkPvM9tb0kdAHSke+w/gOWA5FbZtLo5vk+5W+geYYfvbLq+7vxSFEEIInesvw0chhBCOQRSFEEIIJVEUQgghlERRCCGEUBJFIYQQQkkUhdDvSaor0lW7+P7Jkp7t/JVdWvYsSbsl7W3XPiinge7I6aDDyn7XkNubJN2c2wZKWl/2gFcIFUVRCOHEPQHMOdGF5DTf9laSAh3buxfYY3sk8CYpJZScilsPjCbdtz5H0mk5CHIt6f7+EKqKohB6BUnTJW2StFXSvGIHKmmvpNmSGiWtlXRubh8raWPOl19Wlj0/UtIaSd/n91yaVzG4bG6CRfmBICS9ImlbXs7rFfo1Cthv+6/88wJJcyVtkPRzzmYq5nt4TdLmvKwHcnud0hwYH5IeOjyC7Y1Vnk4tT8xcAkzKfb4N+Nj2ftu7gB20FZXlwLTj/OpDPxNFIfR4kq4gHeFOtD0WaKVt53YW0Gj7amAd6clPgPeAJ22PIe1si/ZFwDu2ryRl5hQ73KuAR0nzbYwAJkoaCtwOjM7LealC9yYCje3ahgE3kOK850o6g3Rk32J7HDAOuF/S8Pz68cDTto9njo9SMmZOB20hpcN2lJj5Y153CFXF+GLoDSYB1wCb8wH8mbSFgR0GPsl//wBYKqkWONv2uty+EPhU0hDgQtvLAGzvA8jL3GS7Of+8lbRj3wjsA+ZL+gKodN3hAlKEdbnFtg8Dv0jaCVwO3ASMkVTk89SSJkU5kNe96zi/k2rJmFUTM223SjogaUiebyOEo0RRCL2BgIW2G47htR3ltlTaYRbKc3JagdNtH5I0nlSU6oGHSSms5f4l7eA76kOxs37E9uojOpTymv7uoF/VFMmYzfnicS1pUpbOEjMHkQpdCBXF8FHoDdYCUySdB6W5ai/JvxtAWzrmncA3tluAPZKuz+13Aevy3BLNkibn5QySVFNtpXleilrbq0hDS2MrvGw7MLJd21RJA/L1ihFAE7AaeChHmyNplNKkOF1Vnpg5hZQO69xenz/bcNLZyKa8znOAInI6hIriTCH0eLa3SXoG+FLSAOAgMBP4lXSUPVrSd6Rx9eLumntI4/k1tCWIQioQ8yS9mJcztYNVDwFW5GsCAh6r8Jr1wGxJclu6ZBPp+sb5wIO290maTxqSaswXhP/kGKaMlPQqqdjVSGoG5tt+nhSR/r6kHaQzhPr8Xf0kaTEpTvoQMNN2a17cjcCqztYZ+rdISQ29mqS9tgd3cx/eAlbaXiNpAfC57SWdvO2Uk7QUaLDd1N19CT1XDB+FcOJeJk0g32MpTS61PApC6EycKYQQQiiJM4UQQgglURRCCCGURFEIIYRQEkUhhBBCSRSFEEIIJf8BQ/+fcrekFEUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e142136cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e14216a240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"adam\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Adam optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y.reshape(train_Y.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.4 - Summary\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **optimization method**\n",
    "        </td>\n",
    "        <td>\n",
    "        **accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **cost shape**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        Gradient descent\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Momentum\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Adam\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        smoother\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "Momentum usually helps, but given the small learning rate and the simplistic dataset, its impact is almost negligeable. Also, the huge oscillations you see in the cost come from the fact that some minibatches are more difficult thans others for the optimization algorithm.\n",
    "\n",
    "Adam on the other hand, clearly outperforms mini-batch gradient descent and Momentum. If you run the model for more epochs on this simple dataset, all three methods will lead to very good results. However, you've seen that Adam converges a lot faster.\n",
    "\n",
    "Some advantages of Adam include:\n",
    "- Relatively low memory requirements (though higher than gradient descent and gradient descent with momentum) \n",
    "- Usually works well even with little tuning of hyperparameters (except $\\alpha$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**References**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  }
 ],
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  "coursera": {
   "course_slug": "deep-neural-network",
   "graded_item_id": "Ckiv2",
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